# Jonathan Christopher Mattingly

- James B. Duke Distinguished Professor
- Professor of Mathematics
- Chair of the Department of Mathematics

### Research Areas and Keywords

##### Analysis

Stochastic Analysis, Malliavin Calculus, Ergodic Theory

##### Biological Modeling

Stochastic and Random PDEs, Stochastic Dynamical Systems, Mathematical Ecology and Evolution, Metabolic and Cellular modeling, Out of equilibrium statistical mechanics

##### Computational Mathematics

Markov Chain Mixing, Stochastic Numerical Methods, High Dimensional Random Algorithms

##### PDE & Dynamical Systems

Stochastic and Random PDEs, Stochastic Dynamical Systems, Malliavin Calculus, Fluid Mechanics, Approximating invariant measures

##### Physical Modeling

Stochastic and Random PDEs, Stochastic Dynamical Systems, Fluid Mechanics

##### Probability

Stochastic and Random PDEs, Stochastic Dynamical Systems, Stochastic Analysis, Malliavin Calculus, Markov Chain Mixing, Ergodic Theory, High Dimensional Random Algorithms, Probability on stratified spaces, Out of equilibrium statistical mechanics, Approximating invariant measures

Jonathan Christopher Mattingly grew up in Charlotte, NC where he attended Irwin Ave elementary and Charlotte Country Day. He graduated from the NC School of Science and Mathematics and received a BS is Applied Mathematics with a concentration in physics from Yale University. After two years abroad with a year spent at ENS Lyon studying nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to attend Princeton University where he obtained a PhD in Applied and Computational Mathematics in 1998. After 4 years as a Szego assistant professor at Stanford University and a year as a member of the IAS in Princeton, he moved to Duke in 2003. He is currently a Professor of Mathematics and of Statistical Science.

His expertise is in the longtime behavior of stochastic system including randomly forced fluid dynamics, turbulence, stochastic algorithms used in molecular dynamics and Bayesian sampling, and stochasticity in biochemical networks.

He is the recipient of a Sloan Fellowship and a PECASE CAREER award. He is also a fellow of the IMS and the AMS.

### Selected Grants

Analysis of Mechanisms of Biochemical Homeostasis awarded by National Science Foundation (Co-Principal Investigator). 2006 to 2010

## Pages

Tempkin, J. O. B., et al. “Trajectory stratification of stochastic dynamics.” *Siam Review*, Society for Industrial and Applied Mathematics, 2016.
Open Access Copy

Herzog, D. P., and J. C. Mattingly. “Noise-induced stabilization of planar flows ii.” *Electronic Journal of Probability*, vol. 20, Oct. 2015. *Scopus*, doi:10.1214/EJP.v20-4048.
Full Text Open Access Copy

Bakhtin, Y., et al. “Regularity of invariant densities for 1D systems with random switching.” *Nonlinearity*, vol. 28, no. 11, Sept. 2015, pp. 3755–87. *Scopus*, doi:10.1088/0951-7715/28/11/3755.
Full Text Open Access Copy

Herzog, D. P., and J. C. Mattingly. “A practical criterion for positivity of transition densities.” *Nonlinearity*, vol. 28, no. 8, July 2015, pp. 2823–45. *Scopus*, doi:10.1088/0951-7715/28/8/2823.
Full Text Open Access Copy

Lawley, S. D., et al. “Stochastic switching in infinite dimensions with applications to random parabolic PDE.” *Siam Journal on Mathematical Analysis*, vol. 47, no. 4, Jan. 2015, pp. 3035–63. *Scopus*, doi:10.1137/140976716.
Full Text Open Access Copy

Huckemann, S., et al. “Sticky central limit theorems at isolated hyperbolic planar singularities.” *Electronic Journal of Probability*, vol. 20, Jan. 2015. *Scopus*, doi:10.1214/EJP.v20-3887.
Full Text Open Access Copy

Munch, E., et al. “Probabilistic Fréchet means for time varying persistence diagrams.” *Electronic Journal of Statistics*, vol. 9, Jan. 2015, pp. 1173–204. *Scopus*, doi:10.1214/15-EJS1030.
Full Text Open Access Copy

Luo, S., and J. C. Mattingly. *Scaling limits of a model for selection at two scales*. 2015.
Open Access Copy

Herzog, David P., and Jonathan Christopher Mattingly. *Noise-Induced Stabilization of Planar Flows II*. Apr. 2014.
Open Access Copy

Lawley, S. D., et al. “Sensitivity to switching rates in stochastically switched ODEs.” *Communications in Mathematical Sciences*, vol. 12, no. 7, Jan. 2014, pp. 1343–52. *Scopus*, doi:10.4310/CMS.2014.v12.n7.a9.
Full Text Open Access Copy

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Jonathan Mattingly created a quantitative Gerrymandering Index for NC that revealed a partisan pattern https://researchblog.... read more »

Geometry of Redisctricting Conference (Nov 2-3) and Workshop (Nov 4-5) will be held at The Searle Center. For additional information, please follow this link: https://sites.duke.edu/... read more »

Team gerrymandering, led by Professor Jonathan Mattingly, feature their latest works in a new webpage: https://www.math.duke.edu/projects/gerrymandering/.... read more »

Bracket math isn’t an exact science, but for years mathematicians have told us that the odds of picking a perfect NCAA tournament bracket are a staggering 1 in 9,223,372,036,854,775,808 (that’s *9.2 quintillion*).
According to Duke math... read more »